Properties

Label 68400gm
Number of curves $1$
Conductor $68400$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("gm1")
 
E.isogeny_class()
 

Elliptic curves in class 68400gm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
68400.u1 68400gm1 \([0, 0, 0, -17625, -610625]\) \(132893440/41553\) \(189325856250000\) \([]\) \(161280\) \(1.4438\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 68400gm1 has rank \(1\).

Complex multiplication

The elliptic curves in class 68400gm do not have complex multiplication.

Modular form 68400.2.a.gm

sage: E.q_eigenform(10)
 
\(q - 3 q^{7} - 2 q^{11} + 2 q^{13} + 4 q^{17} + q^{19} + O(q^{20})\) Copy content Toggle raw display